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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

A Kalman/map filtering (KMF)-aided fast normalized cross correlation (FNCC)-based Wi-Fi fingerprinting location sensing system is proposed in this paper. Compared with conventional neighbor selection algorithms that calculate localization results with received signal strength (RSS) mean samples, the proposed FNCC algorithm makes use of all the on-line RSS samples and reference point RSS variations to achieve higher fingerprinting accuracy. The FNCC computes efficiently while maintaining the same accuracy as the basic normalized cross correlation. Additionally, a KMF is also proposed to process fingerprinting localization results. It employs a new map matching algorithm to nonlinearize the linear location prediction process of Kalman filtering (KF) that takes advantage of spatial proximities of consecutive localization results. With a calibration model integrated into an indoor map, the map matching algorithm corrects unreasonable prediction locations of the KF according to the building interior structure. Thus, more accurate prediction locations are obtained. Using these locations, the KMF considerably improves fingerprinting algorithm performance. Experimental results demonstrate that the FNCC algorithm with reduced computational complexity outperforms other neighbor selection algorithms and the KMF effectively improves location sensing accuracy by using indoor map information and spatial proximities of consecutive localization results.

As the development and integration of mobile computing and sensing technologies, ubiquitous computing integrates the physical world and information space and offers widely available computing and information services [

The RSS fingerprinting method exploits a nonlinear mapping relationship between physical locations and RSS samples from multiple APs. In the off-line phase of the fingerprinting method, specific locations called reference points (RPs) are labeled and RSS samples collected at these RPs are recorded in a database called radiomap. In the on-line phase, on-line RSS data are collected by a Wi-Fi mobile terminal and matched with the RSS data in the radiomap to estimate localization results [

However, using the existing fingerprinting algorithms, multiple on-line RSS samples collected at one location are averaged to compute an RSS mean sample, so useful on-line RSS information is lost in the RSS mean computation. These fingerprinting algorithms fail to make full use of all the on-line RSS information [

Thus, to take advantage of all this information for accuracy improvement, the contributions of this paper are summarized as follows:

First, a fast normalized cross correlation (FNCC) fingerprinting algorithm is proposed to calculate localization coordinates with all the collected on-line RSS samples. It also regards RSS variations of RPs as weights for correlation coefficient computations to precisely select RPs. Compared with the basic normalized cross correlation (NCC) algorithm, which is computationally expensive, the proposed FNCC algorithm greatly reduces computational complexity while maintaining the same accuracy as the NCC, which is higher than those of conventional neighbor selection algorithms.

Second, indoor map information is used by a proposed map matching algorithm. A calibration model that represents pedestrian walkways is integrated into an indoor map. Then a map image matrix is created for the map matching algorithm. Based on the building interior structure, unreasonable location coordinates are corrected by the map matching algorithm to the calibration model and therefore more accurate location coordinates are obtained.

Third, based on the map matching algorithm, a Kalman/map filtering (KMF) is proposed to process fingerprinting results using indoor map information and spatial proximities of consecutive localization results. Through nonlinearizing the linear prediction process of Kalman filtering (KF) by the map matching algorithm, more accurate prediction locations are obtained for the KMF. This greatly improves the KMF performance of increasing location sensing accuracy.

The remainder of this paper is structured as follows: in Section 2, related work is discussed. The proposed FNCC fingerprinting algorithm, map matching algorithm and KMF are described in detail in Section 3. Section 4 gives the experimental setup, results and analyses. Finally, the paper is concluded in Section 5.

To the best of our knowledge, NCC has not been applied as an RSS fingerprinting algorithm for location-sensing computing. However, Xiao

In the area of image similarity measurements, NCC has been used extensively [

Regarding the filtering algorithms for processing Wi-Fi fingerprinting results, particle filtering (PF) and KF are commonly used. As a linear filtering algorithm, KF processed the localization results of the ANN, nearest neighbor and propagation model [

However, PF-based algorithms are usually time-consuming, especially when the number of particles is considerable. Compared with the PF-based algorithms, the KF computes much faster. Because it works iteratively and just requires a prediction state and measurement data. Thus, through combining a presented map matching algorithm and the KF, a KMF is proposed in this paper. The KF linear prediction process is nonlinearized by the map matching algorithm. With the advantages of both the map matching algorithm and KF, the proposed KMF effectively improves location sensing accuracy with only Wi-Fi fingerprinting results as measurement data. Regarding the limited hardware resources and power of Wi-Fi mobile terminals, the KMF is suitable to be embedded into the Wi-Fi mobile terminals for practical applications.

In Section 3.1, the proposed FNCC fingerprinting algorithm is described in detail. The FNCC not only makes full use of off-line and on-line RSS information, but also greatly reduces computational complexity, especially for calculating the NCC denominator, while maintaining high fingerprinting accuracy. A map matching algorithm is presented in Section 3.2. An indoor map is processed and converted into an image matrix with a calibration model for coordinate corrections. With the image matrix, the map matching algorithm can be used as an independent algorithm to correct unreasonable location coordinates. With the integration of the map matching algorithm into the KF, the proposed KMF algorithm is detailed in Section 3.3. The KMF effectively improves location sensing accuracy with indoor map information and spatial proximities of consecutive localization results. For convenience, key symbols used in this paper are listed in

NCC has been widely used for many image processing applications because of its abilities to cope with noisy images. In this paper, it is applied to measure the correlation degree between collected on-line RSS data and RSS data of an RP using a correlation coefficient, which ranges from −1 to 1. The correlation coefficient is equal to −1 in the case of a perfect negative correlation, 0 no correlation and 1 a perfect positive correlation [_{l}_{l}_{rss} and _{l}_{l}

After all these _{i}_{1}_{L}

For computing one localization result, the

As we know, it is much faster for a computer to execute a multiplication operation than to execute a square root operation, so

Compared with the basic NCC computation denoted by _{rss} and _{l}

For calculating one squared correlation coefficient

To improve location sensing performance, an indoor map integrated with a calibration model is processed for the proposed map matching algorithm. The indoor map is derived from an indoor building plan of computer aided design (CAD) and the calibration model is comprised of straight lines that represent pedestrian walkways. According to the building interior structure, unreasonable localization results are corrected to the calibration model for accuracy improvement.

First, the original indoor map and the indoor map integrated with the calibration model are saved as two JPEG gray-scale images _{model} and _{no_model}, respectively. Using _{model} and _{no_model}, respectively. The size of the binary image matrices is proportionally adapted according to the size of the building plan.

_{threshold} is the threshold.

In the two binary images _{model} and _{no_model}, the pixel points of the calibration model and building structure are represented by 0 and the pixel points of people activity areas are represented by 1. To distinguish the calibration model from the building structure, a new image matrix _{match} is created by _{match} is directly used by the map matching algorithm.

In the new image matrix _{match}, the pixel points of people activity areas and building structure are still represented by 1 and by 0, respectively, but the pixel points of calibration model are represented by −1. So the calibration model is recognized by −1 and unreasonable localization results can be corrected to the calibration model. The flow chart of the map matching algorithm is shown in

Process the available indoor map information and create accurate building plan image matrix _{match} for map matching.

Transform the _{n}_{n}_{n}_{match}.

If

If building structure barriers exist between the _{n}

Calculate the pixel point
_{n}_{n}_{−}_{1}_{mid}

Transform the localization pixel point

In the area of Wi-Fi fingerprinting location sensing, KF has been applied to process localization results calculated by fingerprinting algorithms. The KF firstly predicts a user's movement state at the present time step by using the previous movement state. When a present measurement result that is a fingerprinting result is obtained, the measurement result is used to correct the predicted movement state. In this process, spatial proximities of consecutive localization results are employed by the KF. However, one drawback of the KF is its linear prediction model cannot precisely predict people movement in indoor environments, so the map matching algorithm is employed by the KMF to nonlinearize the linear prediction process.

The general KF linear process and measurement equations are as follows:
_{n}_{n}_{n}_{n}

The KF operates in two distinct phases: the time update and measurement update. In the time update phase, the new state vector and its uncertainty at the present time step are predicted, which is given by:

In the measurement update phase, the predicted vector is corrected and the KF parameters are updated for the next iteration when a measurement result is obtained. The process is denoted by:
_{n̄} is the _{n} is the _{n̄} is the covariance matrix of the _{n}_{n}

The KF linear prediction denoted by _{map}(·) so the nonlinear relationship between the _{n}=_{n}_{n}

Setting the _{n̄} as follows:
_{n̄} =(_{x}_{y}_{n}_{̄} is the velocity vector, _{x}_{y}

Subsequently, the formula for calculating the

The diagram of the proposed KMF is shown in

The experimental floor is a rectangular area of 24.9 m × 66.4 m. For communication purposes on the floor, nine Linksys WAP54G APs were deployed. As shown in

The experimental trajectory spanned Point A in Room 1211 to Point B in the 3 m width corridor. Installed a software named NetStumbler, an ASUS A8F laptop collected RSS samples with a sampling rate of two RSS samples per second. For establishing a radiomap, RSS samples were collected at 91 RPs in Room 1211 and the corridor and 300 RSS samples were recorded within 150 s at each RP. Along the experimental trajectory, a total of 6,500 RSS testing samples were collected at 65 testing points (TPs) with 0.6 m gaps.

The performance of the FNCC algorithm is evaluated with the collected RSS testing data. For comparison, the mean errors of the FNCC and conventional KNN algorithms are calculated with the numbers of on-line RSS samples

Considering the number and distribution of RPs as well as computational complexity, parameter

Regarding the on-line computational complexity, some terms in both the denominators and numerators of _{i,j}_{rss}), (_{i,j,l}_{1}) and

In this paper, the threshold _{threshold}

Through map matching, the mean errors of the KNN and FNCC algorithms are reduced from 3.00 m and 2.71 m to 2.96 m and 2.59 m, respectively. With all the 6,500 RSS testing samples, the localization results of the KNN, WKNN and FNCC algorithms corrected by the map matching algorithm are listed in

With the map matching algorithm, the KF linear prediction process is nonlinearized by the proposed KMF. Accurate prediction locations corrected by the map matching algorithm increase the accuracy of the KMF estimates after measurement corrections. Based on the KF theory, the proposed KMF process equation is set as follows:
_{x}_{y}^{2}. _{n}_{n}

The KMF measurement equation is given by:
_{x}_{y}_{n}

With all the 6,500 RSS testing samples, the mean errors of KNN + KF, WKNN + KF and FNCC + KF are 2.65 m, 2.65 m and 2.41 m, respectively. By comparison, the mean errors of the KNN + KMF, WKNN + KMF and FNCC + KMF are 1.88 m, 1.90 m and 1.87 m, respectively. Their standard deviations are 1.24 m, 1.27 m and 1.24 m, respectively. These results indicate that the KMF outperforms the KF. Combined with

In this paper, a KMF-aided FNCC Wi-Fi fingerprinting indoor location sensing system is proposed. Because the NCC is able to make full use of off-line RSS variations of RPs and all the collected on-line RSS samples, the NCC fingerprinting algorithm outperforms the conventional KNN and WKNN fingerprinting algorithms that calculate a localization result with only an on-line RSS mean sample. However, the computational cost of the basic NCC algorithm is very expensive, so an FNCC algorithm is developed. It greatly reduces computational complexity while maintaining the same high accuracy as the basic NCC algorithm. Through integrating a proposed map matching algorithm into the KF, a KMF is proposed to improve location sensing accuracy. Using available indoor map information, the proposed map matching algorithm corrects unreasonable locations computed by the KF linear state prediction process to a calibration model, which represents pedestrian walkways. Based on the corrected locations, the KMF can calculate more accurate localization results using measurement data than the KF. The experimental results confirm both that the FNCC significantly reduces computational complexity of correlation computations without accuracy decreases and that KMF effectively improves location sensing accuracy by using indoor map information and spatial proximities of consecutive localization results.

The authors gratefully thank the referees for their constructive and insightful comments. This work was supported by National High-Tech Research & Development Program of China under Grant 2012AA120802 and by National Natural Science Foundation of China under Grant 61071105 and 611011220.

The authors declare no conflict of interest.

Flow chart of map matching algorithm.

Diagram of Kalman/map filtering.

Experimental area plan.

(

(

(

(

Cumulative probabilities of various algorithms.

Key symbols used in this paper.

Number of labeled RPs | |

Number of deployed APs | |

Number of on-line RSS samples for computing one result | |

Number of selected RPs | |

On-line RSS matrix for computing localization coordinates | |

_{l} |
Created RSS matrix of |

_{l} |
Correlation coefficient between RSS matrices _{l} |

_{i,j} |
RSS numerical value in |

_{i,j,l} |
RSS numerical value in _{l} |

_{match} |
Image matrix for map matching |

Performance comparison of KNN, WKNN, NCC, and FNCC algorithms.

KNN | 2.77 | 1.91 | 39.6 | 64.7 |

WKNN | 2.74 | 1.91 | 41.2 | 65.4 |

NCC with |
2.60 | 1.93 | 45.9 | 68.9 |

FNCC with |
2.60 | 1.93 | 45.9 | 68.9 |

FNCC with |
2.60 | 1.93 | 45.9 | 68.9 |

Computational complexity comparison.

KNN | |||

WKNN | |||

NCC with |
|||

FNCC with |
0 | ||

FNCC with |
0 |

Comparison of map matching results.

KNN + Map | 2.62 | 1.90 | 43.5 | 67.4 |

WKNN + Map | 2.57 | 1.89 | 45.4 | 68.7 |

FNCC + Map | 2.39 | 1.85 | 51.0 | 73.0 |

Comparison of KNN, WKNN, FNCC, and their processed results by map matching and KMF algorithms.

KNN | 2.77 | 1.91 | 39.6 | 64.7 |

WKNN | 2.74 | 1.91 | 41.2 | 65.4 |

FNCC | 2.60 | 1.93 | 45.9 | 68.9 |

KNN + Map | 2.62 | 1.90 | 43.5 | 67.4 |

WKNN + Map | 2.57 | 1.89 | 45.4 | 68.7 |

FNCC + Map | 2.39 | 1.85 | 51.0 | 73.0 |

KNN + KMF | 1.88 | 1.24 | 61.0 | 83.0 |

WKNN + KMF | 1.90 | 1.27 | 61.6 | 83.0 |

FNCC + KMF | 1.87 | 1.24 | 61.3 | 85.1 |